Based on a Pade approximation, a wide-angle parabolic equation method is introduced for computing the multiobject radar cross section （RCS） for the first time. The method is a paraxial version of the scalar wave equ...Based on a Pade approximation, a wide-angle parabolic equation method is introduced for computing the multiobject radar cross section （RCS） for the first time. The method is a paraxial version of the scalar wave equation, which solves the field by marching them along the paraxial direction. Numerical results show that a single wide-angle parabofic equation run can compute multi-object RCS efficiently for angles up to 45 ° . The method provides anew and efficient numerical method for computation electromagnetics.展开更多
Parabolic equation （PE） method is an efficient tool for modelling underwater sound propagation, particularly for problems involving range dependence. Since the PE method was first introduced into the field of underw...Parabolic equation （PE） method is an efficient tool for modelling underwater sound propagation, particularly for problems involving range dependence. Since the PE method was first introduced into the field of underwater acoustics, it has been about 40 years, during which contributions to extending its capability has been continuously made. The most recent review paper surveyed the contributions made before 1999. In the period of 2000-2016, the development of PE method basically focuses on seismo-acoustic problems, three-dimensional problems, and realistic applications. In this paper, a review covering the contribution from 2000 to 2016 is given, and what should be done in future work is also discussed.展开更多
A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method a...A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.展开更多
The multigrid algorithm in [13] is developed for solving nonlinear parabolic equations arising from the finite element discretization. The computational cost of the algorithm is approximate O(NkN) where N-k is the dim...The multigrid algorithm in [13] is developed for solving nonlinear parabolic equations arising from the finite element discretization. The computational cost of the algorithm is approximate O(NkN) where N-k is the dimension of the finite element space and N is the number of time steps.展开更多
The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundl...The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.展开更多
基金This project was partially supported by the National Natural Science Foundation of China (60371041).
文摘Based on a Pade approximation, a wide-angle parabolic equation method is introduced for computing the multiobject radar cross section （RCS） for the first time. The method is a paraxial version of the scalar wave equation, which solves the field by marching them along the paraxial direction. Numerical results show that a single wide-angle parabofic equation run can compute multi-object RCS efficiently for angles up to 45 ° . The method provides anew and efficient numerical method for computation electromagnetics.
基金Project supported by the Foundation of State Key Laboratory of Acoustics,Institute of Acoustics,Chinese Academy of Sciences(Grant No.SKLA201303)the National Natural Science Foundation of China(Grant Nos.11104044,11234002,and 11474073)
文摘Parabolic equation （PE） method is an efficient tool for modelling underwater sound propagation, particularly for problems involving range dependence. Since the PE method was first introduced into the field of underwater acoustics, it has been about 40 years, during which contributions to extending its capability has been continuously made. The most recent review paper surveyed the contributions made before 1999. In the period of 2000-2016, the development of PE method basically focuses on seismo-acoustic problems, three-dimensional problems, and realistic applications. In this paper, a review covering the contribution from 2000 to 2016 is given, and what should be done in future work is also discussed.
文摘A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.
文摘The multigrid algorithm in [13] is developed for solving nonlinear parabolic equations arising from the finite element discretization. The computational cost of the algorithm is approximate O(NkN) where N-k is the dimension of the finite element space and N is the number of time steps.
文摘The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.
